This phase I trial studies the side effects of HERV-E TCR transduced CD8+ / CD34+ T-cells in treating patients with clear cell renal cell cancer that has spread to other places in the body. HERV-E is a viral molecule of the HERVs family that becomes active in cancer cells and has been found in the surface of kidney tumor cells (not in healthy human normal cells). The incorporation of HERV-E into lymphocytes (T cells) may enable the immune system to recognize and fight kidney cancer cells.

Inclusion Criteria

Patients must have histologically confirmed renal cell carcinoma (RCC) with clear-cell component by the Laboratory of Pathology of the National Institutes of Health (NIH) prior to entering this study

Patients must be HLA-A 11:01 positive (confirmed by HLA typing at the NIH Department of Transfusion Medicine [DTM])

Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 and have disease progression during or after the last treatment regimen and within 6 months before study enrollment

Patients must have received at least one antiangiogenic drug and an immune-checkpoint inhibitor (i.e. nivolumab) unless the patient has contraindications to receiving these medications, the agents are not available to the patient, or the patient declines to receive these drugs due to personal preference

Patients must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, the duration of study participation and 180 days (female patients) or 90 days (male patients) after the end of the treatment if sexually active and able to bear or beget children. In addition, male patients must refrain from sperm donation for 90 days after the final dose of investigational product. Female patients must refrain from egg cell donation for 180 days after the final dose of investigational product

Patient must have an anticipated life expectancy of at least 3 months

Patients must have a performance status of 0 or 1 Eastern Cooperative Oncology Group (ECOG) performance status (PS) scale

Patients must have a caregiver willing to stay with them during the first month of treatment (30 days +/- 5 days)

Patients receiving treatment with bisphosphonates or denosumab are eligible for enrollment if on a stable dose for >= 4 weeks

Serology:
* Seronegative for human immunodeficiency virus (HIV) antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus be less responsive to the experimental treatment and more susceptible to its toxicities)
* Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by reverse transcription-polymerase chain reaction (RT-PCR) and be hepatitis C virus (HCV) ribonucleic acid (RNA) negative

Patients must have the ability to provide written informed consent prior to study specific screening procedures, with the understanding that the patient has the right to withdraw from the study at any time

Exclusion Criteria

Patients must not have had standard of care anti-VEGFR therapy (mean half-life around 30 hours), mTOR inhibitors (mean half-life around 30 hours), radiotherapy, or major surgery within the last 2 weeks prior to T-cell infusion. For PD-1/PD-L1 inhibitors or CTLA-4 inhibitors, a 4-week period must have elapsed before T-cell infusion. For recent experimental therapies a 28-day period must have elapsed before infusing expanded T-cells

Patients with active central nervous system (CNS) involvement by malignancy either by imaging or cerebrospinal fluid involvement or biopsy-proven (due to poor prognosis and potential for neurological dysfunction that would confound evaluation of neurological and other adverse events) except for:
* Patients with single brain metastases of < 1 cm treated with either stereotactic or gamma knife radiotherapy and remained stable on MRI for 2 weeks are eligible
* Patients with 3 or fewer brain metastases of < 1 cm treated with either stereotactic or gamma knife radiotherapy and remained stable on MRI for 4 weeks are eligible
* Patients with surgically resected brain metastases and no evidence of active disease in the CNS at the time of screening evaluation are eligible
* These patients may be enrolled at the discretion of the principal investigator

Patients with hypercalcemia (> 10 mg/dL) of malignancy

Any prior grade >= 3 immune-related adverse event (irAE) while receiving immunotherapy, including anti-CTLA4 treatment, or any unresolved irAE > grade 1. Note: active or history of vitiligo or hypothyroidism will not be a basis for exclusion

Patients with second malignancies in addition to their clear cell RCC are not eligible if the second malignancy has required treatment (including maintenance therapy) within the past 4 years or is not in complete remission. There are exceptions to this criterion: successfully treated non-metastatic basal cell, squamous cell skin carcinoma, in situ non-invasive cervical cancer and in situ non-invasive breast cancer

Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant

Systemic corticosteroid steroid therapy of any dose is not allowed within 14 days prior to the required leukapheresis, or the initiation of the conditioning chemotherapy regimen. The following are exceptions to this criterion:
* Intranasal, inhaled, and topical steroids
* Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent
* Steroids as premedication for hypersensitivity reactions (e.g., computed tomography [CT] scan premedication)
** In the case of short-term use of systemic corticosteroids (less than 24 hours within 28 days) of greater than 10 mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the leukapheresis is 7 days

History of severe immediate hypersensitivity reaction to any of the agents used in this study

Unable to understand the investigational nature of the study or give informed consent and does not have a legally authorized representative or surrogate that can provide informed consent

Any condition that, in the opinion of the investigator, would interfere with evaluation of the investigational product or interpretation of subject safety or study results